Isomorphisms of symplectic groups over commutative rings
The isomorphisms of symplectic groups over arbitrary commutative rings are described. Let R, \(R_ 1\) be commutative rings. It is proved in particular, that every isomorphism between the groups G and \(G_ 1\) where \(ESp_{2n}(R)\leq G\leq Sp_{2n}(R),\quad ESp_{2m}(R_ 1)\leq G_ 1\leq Sp_{2m}(R_ 1),\quad n,m\geq 3\) is standard; it gives an affirmative answer to the question 8.46 by Yu. I. Merzlyakov from The Kourovka Notebook [8th ed. (1982; Zbl 0509.20001)].
scientific article; zbMATH DE number 3861437
scientific article